Question

Let M = ( (−3 1 3 4), (1 2 −1 −2), (−3 8 4 2))

14. (3 points) Let B1 be the basis for M you found by row reducing M and let B2 be the basis for M you found by row reducing M Transpose . Find the change of coordinate matrix from B2 to B1.

Answer #1

Let A = [1 5 ; 3 1 ; 2 -4] and b = [1 ; 0 ; 3] (where semicolons
represent a new row)
Is equation Ax=b consistent?
Let b(hat) be the orthogonal projection of b onto Col(A). Find
b(hat).
Let x(hat) the least square solution of Ax=b. Use the formula
x(hat) = (A^(T)A)^(−1) A^(T)b to compute x(hat). (A^(T) is A
transpose)
Verify that x(hat) is the solution of Ax=b(hat).

Consider the following matrix.
A =
4
-1
-1
2
6
-3
6
4
1
Let B = adj(A). Find b31,
b32, and b33. (i.e., find
the entries in the third row of the adjoint of A.)

A=
2
-3
1
2
0
-1
1
4
5
Find the inverse of A using the method: [A | I ] → [ I | A-1 ].
Set up and then use a calculator (recommended). Express the
elements of A-1 as fractions if they are not already integers. (Use
Math -> Frac if needed.) (8 points)
Begin the LU factorization of A by determining a first
elementary matrix E1 and its inverse E1-1. Identify the associated
row operation. (That...

Let T(V)=AV be a linear transformation where A=(3 -2 6 -1 15, 4
3 8 10 -14, 2 -3 4 -4 20)
a.) construct a basis of the kernal T
b.) calculate the basis of the range of T
c.) determine the rank and nullity of T

Suppose B = {b1,b2} is basis for linear space V and C =
{⃗c1,⃗c2,⃗c3} is a basis for linear space W. Let T : V → W be a
linear trans- formation with the property that ⃗ T ( b 1 ) = 3 ⃗c 1
+ ⃗c 2 + 4 ⃗c 3 , ⃗ T ( b 2 ) = 4 ⃗c 1 + 2 ⃗c 2 − ⃗c 3 . Find the
matrix M for T relative to...

Let C = column matrix [1 2 3 1] and D = row matrix[−1 2 1 4] .
Prove that (CD)^10 is the same as C(DC)^9D and do the calculation
by hand.

1. Let ?(?)=−?4−4?3+8?−1. Find the open intervals on which ? is
concave up (down). Then determine the ?-coordinates of all
inflection points of ?.
2. Find the x-values of all inflection points for the graph
?(?)=2?4+18?3−30?2+15f(x)=2x4+18x3−30x2+15. (Give your answers as a
comma separated list, e.g., 3,-2.)
3. Let f(x)=1/4x2+7. Find the open intervals on which ?f is
concave up (down). Then determine the ?x-coordinates of all
inflection points of ?.
4. Let ?(?)=6?−3/?+4 Find the open intervals on which ?f...

[ 1
3 9 -7
0 1 4 -3
2 1 -2 1]
find basis for col A. dimension of col A
find basis for nul A. dimension of nul A
find basis for row A. dimension of row A
asap plz, tyouuu

Let A be a 2x2 matrix
6 -3
-4 2
first, find all vectors V so the distance between AV and the
unit basis vector e_1 is minimized, call this set of all vectors
L.
Second, find the unique vector V0 in L such that V0 is
orthogonal to the kernel of A.
Question: What is the x-coordinate of the vector V0 equal to.
?/?
(the answer is a fraction which the sum of numerator and
denominator is 71)

3. Write the matrix in row-echelon form:
1
2
-1
3
3
7
-5
14
-2
-1
-3
8

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